How to "factory reset" iCloud?

No. But, you can delete all of the individual files on iCloud.com.

Basically_Luka Said:

"How to 'factory reset' iCloud?: I don’t have anything on iCloud Drive. It is empty. But it still restores from somewhere when I Sign In with Apple ID"

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Verify your Devices:

See the device associated to this account. One or more those listed items may be causing this. Go here: Check your Apple ID Device List to See where you're Signed in - Apple Support

If you do not restore your backup, or if you do not sync to iCloud, there will be nothing to restore. But some information is still attached to your Apple ID (eg. purchase history, etc. ) which cannot be removed.

Basically_Luka Said:

"Been there already. 2 devices only. Apple Watch and iPhone. + AirPods which don’t have backups."

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New iCloud Sessions:

Sign out of iCloud on both devices to disassociate them from your account, seeing if this ends. Then log back in to iCloud, with all new login sessions.

Settings> Apple ID > iCloud > Backup to turn it off

Settings > Apple ID > Manage Storage > backups > your device name > delete backup

Basically_Luka Said:

"How to 'factory reset' iCloud?: Is there any way to literally delete everything and give iCloud and my iPhone 'new life'?"

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Downloading All of This:

Perform my User Tip: Getting a Quick and Direct "iCloud Drive-to-External Hard Drive" Download - User Tip

Once downloaded, delete it all from iCloud.

It won't, unless you still have the files in iCloud or in a backup that you restore.